Syllogism: Concepts, Formulas, and Clear Examples
Syllogisms test deductive logic from statements like ‘All A are B’ and ‘Some B are C.’ You decide which conclusions must follow, may follow, or do not follow. Venn diagrams are the most reliable visual for placement exams.
Modern papers use only a few statement types: All, Some, No, Some not. Combine with conversion rules (Some A are B ↔ Some B are A; No A are B ↔ No B are A) but never illicitly convert ‘All A are B’ to ‘All B are A.’
Statement types and Venn sketches
- All A are B: circle A inside B.
- No A are B: two separate circles.
- Some A are B: overlapping region marked.
- Some A are not B: part of A outside B.
Valid immediate inferences
Invalid (illicit conversion)
- All A are B → Some B are A (if A exists).
- No A are B → No B are A.
- Some A are B → Some B are A.
Chaining two statements
All A→B and All B→C ⇒ All A→C. Some A→B and All B→C ⇒ Some A→C. No A→B and All B→C ⇒ Some C are not A (careful wording).
Example — Two-statement set
All cats are mammals. Some mammals are pets.
Cannot conclude All cats are pets or Some cats are pets necessarily from these alone—the overlap of mammals and pets may exclude cats in Venn unless ‘some mammals’ hits the cat region.
Either/or conclusions
- Complementary pair: exactly one may be true in some formats—read instructions.
Possibility cases
‘Possibility’ questions ask if a scenario can exist consistent with diagrams—not if it must.
MCQ conclusion labels
- Only I follows / Both I and II / Neither—evaluate each conclusion independently.
Step-by-step method for exam questions
- Draw minimal Venn for each statement.
- Merge diagrams on shared categories.
- Read each conclusion against the merged figure.
- Mark Must follow / Does not follow / Possible only.
- Apply conversion rules only where valid.
- Pick the option code matching your tags.
Formula cheat sheet
| Situation | Formula | When to use |
|---|---|---|
| All + All | All A→C | Chain through B |
| Some + All | Some A→C | Existential chain |
| No + All | No A→C | Negative chain |
| Illicit All converse | Invalid | Trap conclusion |
| Some not | Part of A outside B | Partial exclusion |
Frequently asked questions
Do cats exist if ‘All cats are mammals’?
In aptitude syllogism, existential import is usually assumed—A is non-empty unless stated.
Venn or rules table?
Venn for accuracy; memorize only standard chains for speed.
Three statement syllogism?
Same merge process; solve middle term links first.
Practice on this platform
Use 4 practice sets (10 MCQs, detailed solution after each answer) and 2 timed mocks (20 minutes) on this topic to convert formulas into speed and accuracy.